石墨烯纳米环的电子结构和持续电流

Electronic Structure and Persistent Current in Graphene Rings

摘要: 基于紧束缚理论，研究了石墨烯纳米环的电子结构和磁响应特性。计算结果表明当存在垂直磁场时，由于谷间散射,能谱中每个能带由六条能级组成。根据环的电子结构，石墨烯纳米环可以分为金属环和半导体环。在金属环中，持续电流随着磁通增大呈现线性变化关系。然而，半导体环的持续电流随着磁通增大呈现正弦函数关系。无论是金属还是半导体石墨烯环，磁通驱动下的电子都沿着环做逆时针运动，因而呈现出抗磁特性。

Abstract: The electronic structure and persistent current of graphene rings have been studied using the tight-binding model. Our results show that in the presence of a perpendicular magnetic field, en-ergy spectrum can be grouped into bands with six levels per band owing to inter-valley scattering. According to degeneracy of energy level at the Fermi energy, the graphene rings are divided into two groups, metallic and semiconducting rings. In metallic rings, the persistent current within a flux period changes linearly with magnetic flux ϕ, while it is a sinusoidal periodical function of ϕ in semiconducting rings. Both metallic and semiconducting rings exhibit diamagnetic response, because the electrons driven by magnetic flux flow anticlockwise along the rings.

文章引用：缪晶晶, 张潇元, 史友进, 张海洋, 徐宁. 石墨烯纳米环的电子结构和持续电流[J]. 应用物理, 2017, 7(3): 71-76. https://doi.org/10.12677/APP.2017.73010

参考文献

[1]	Novoselov, K.S., Geim, A.K., Morozov, S.V., et al. (2005) Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature, 438, 197-200. https://doi.org/10.1038/nature04233
[2]	Zhang, Y.B., Tan, Y.W., Stormer, H.L. and Kim, P. (2005) Experimental Observation of the Quantum Hall Effect and Berry Phase in Graphene. Nature, 438, 201-204. https://doi.org/10.1038/nature04235
[3]	Berger, C., Song, Z., Li, X., Wu, X., Brown, N., Naud, C., et al. (2006) Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science, 312, 1191-1996. https://doi.org/10.1126/science.1125925
[4]	Berger, C., Song, Z., Li, T.B., et al. (2004) Ultrathin Epitaxial Graphite: 2D Elextron Gas Properties and Route toward Graphene-Based Nanoelectronics. The Journal of Physical Chemistry B, 108, 19912-19916. https://doi.org/10.1021/jp040650f
[5]	Hiura, H. (2004) Tailoring Graphite Layers by Scanning Tunneling Microscopy. Applied Surface Science, 222, 374- 381.
[6]	刘守鹏, 等. 人工裁剪制备石墨纳米结构[J]. 物理学报, 2005, 54(9): 4251-4255.
[7]	Berger, C., Song, Z., Li, X., Wu, X., Brown, N., Naud, C., Mayou, D., Li, T., Hass, J., Marchenkov, A.N., Conrad, E.H., First, P.N. and Heer, A. (2006) Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science, 312, 1191-1196. https://doi.org/10.1126/science.1125925
[8]	Novoselov, K.S., Jiang, Z., Zhang, Y., Morozo, S.V., Stormer, H.L., Zeitler, U., Maan, J.C., Boebinger, G.S., Kim, P. and Geim, A.K. (2007) Room-Temperature Quantum Hall Effect in Graphene. Science, 315, 1379-1381. https://doi.org/10.1126/science.1137201
[9]	Ponomarenko, L.A., Schedin, F., Katsnelson, M.I., Yang, R., Hill, W., Novolevov, K.S. and Geim, A.K. (2008) Chaotic Dirac Billiard in Graphene Quantum Dots. Science, 320, 356-358. https://doi.org/10.1126/science.1154663
[10]	Shen, T., Wu, Y.Q., Capano, M.A., Robickinson, L.P., Engel, L.W. and Ye, P.D. (2008) Magneto-Conductance Oscillations in Graphene Antidot Arrays. Applied Physics Letters, 93, 122102-122104. https://doi.org/10.1063/1.2988725
[11]	Obradovic, B., Kotlyar, R., Heinz, F., Matagne, P., Rakshit, T., Giles, M.D., Stettler, M.A. and Nikonov, D.E. (2006) Analysis of Graphene Nanoribbons as a Channel Material for Field-Effect Transistors. Applied Physics Letters, 88, 142102-142105. https://doi.org/10.1063/1.2191420
[12]	Echtermeyer, T.J., Lemme, M.C., Bolten, J., Baus, M., Ramsteiner, M. and Kurz, H. (2007) Graphene Field-Effect Devices. The European Physical Journal Special Topics, 148, 19-26. https://doi.org/10.1140/epjst/e2007-00222-8
[13]	Areshkin, D.A. and White, C.T. (2007) Building Blocks for Integrated Graphene Circuits. Nano Letters, 7, 3253-3259. https://doi.org/10.1021/nl070708c
[14]	Recher, P., Trauzettel, B., Rycerz, A., Blanter, Y.M., Beenakker, C.W.J. and Morpurgo, A.F. (2007) Aharonov-Bohm Effect and Broken Valley Degeneracy in Graphene Rings. Physical Review B, 76, 23540-235404. https://doi.org/10.1103/PhysRevB.76.235404
[15]	Bahamon, D.A., Pereira, A.L.C. and Schulz, P.A. (2009) Inner and Outer Edge States in Graphene Rings: A Numerical Investigation. Physical Review B, 79, 125414-125421. https://doi.org/10.1103/PhysRevB.79.125414
[16]	Ma, M.M., Ding, J.W. and Xu, N. (2009) Odd-Even Width Effect on Persistent Current in Zigzag Hexagonal Graphene Rings. Nanoscale, 1, 387-390. https://doi.org/10.1039/b9nr00044e
[17]	Xu, N., Chen, Q., Tian, H.Y., Wang, B.L. and Ding, J.W. (2016) Diamagnetism in Zigzag Hexagonal Graphene Rings. Physics Letters A, 380, 1102-1104.
[18]	Xu, N., Wang, B.L., Shi, D.N., Wang, Y.Z. and Zhang, C. (2012) Fano Resonance in Graphene Anti-Dot and Periodic Graphene Anti-Dot Arrays. Physics Letters A, 376, 3322-3325.
[19]	Louis, E., Verges, J.A. and Chiappe, G. (1998) Dimensional and Band-Structure Effects on Persistent Currents in Mesoscopic Metallic Rings. Physics Letters B, 58, 6912-6919. https://doi.org/10.1103/PhysRevB.58.6912
[20]	Omidi, M. and Faizabadi, E. (2015) Energy Spectrum and Persistent Current in an Armchair Hexagonal Graphene Ring in the Presence of Vacancies, Rashba and Zeeman Interactions. The European Physical Journal B, 88, 30. ttps://doi.org/10.1140/epjb/e2014-50607-1